The Mann–Whitney effect is a nonparametric measure for comparing the distribution between two groups, which can be estimated by right-censored data. However, the traditional estimator of the Mann–Whitney effect based on the Kaplan–Meier estimators can be inconsistent when the independent censoring assumption fails to hold. Investigation is made on the asymptotic bias of the traditional estimator of the Mann–Whitney effect when the independent censoring assumption is violated due to dependence between survival time and censoring time. A new estimator of the Mann–Whitney effect is proposed by applying the copula-graphic estimator to adjust for the effect of dependent censoring. The proposed estimator and test are consistent when the assumed copulas for the two groups are correct. Some consistency properties under misspecified copulas are also given. Simulations are conducted to verify the proposed method under possible misspecification on copulas. The method is illustrated by a real data set. We provide an R function “MW.test” to implement the proposed estimator and test.

中文翻译：

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依赖删失下双样本问题中曼-惠特尼效应的估计

Mann-Whitney 效应是一种用于比较两组之间分布的非参数度量，可以通过右删失数据进行估计。然而，当独立审查假设不成立时，基于 Kaplan-Meier 估计量的 Mann-Whitney 效应的传统估计量可能不一致。当独立审查假设因生存时间和审查时间之间的依赖性而被违反时，对传统的 Mann-Whitney 效应估计量的渐近偏差进行了调查。提出了一种新的 Mann-Whitney 效应估计量，通过应用 copula-graphic 估计量来调整相关审查的影响。当两个组的假定 copula 正确时，建议的估计量和测试是一致的。还给出了错误指定的 copula 下的一些一致性属性。进行模拟以验证在可能错误指定 copula 的情况下所提出的方法。该方法通过一个真实的数据集来说明。我们提供了一个 R 函数“MW.test”来实现建议的估计器和测试。